Aircraft computer



Aug. 21, 1951 R. c. KNOWLES ET AL AIRCRAFT COMPUTER 5 Sheets-Sheet 1 Filed July 21, 1943 EC W-T ALA 4 E d 5.5 iBYg R. C. KNOWLES ET AL Aug. 21, 1951 AIRCRAFT COMPUTER 5 Sheets-Sheet 2 Filed Jul 21, 1943 MUN RN Wm @R m NE Q Aug. 21, 1951 Filed July 21, 1945 R. C. KNOWLES ET AL AIRCRAFT COMPUTER 5 Sheets-Sheet 5 all Aug. 21, 1951 R. c. KNOWLES ETAL AIRCRAFT COMPUTER Filed July 21, 1943 5 Sheets-Sheet 4 INVENTORS 1?. C. KNOWLES 14/.7; WHITE 14. HARRl-SQJR.

Patented Aug.

2,564,ii L 18 AIRCRAFT COMPUTER Richard C. Knowles,- New York, Walter T. White, Hempstead, Herbert Harris, Jr., Cedarhurst, Edward J. Nagy, Garden City, and Edmund B. Hammond, Jn, Brooklyn, 1?. Y., assignors to The Sperry Corporation, a corporation of Dela.-

ware

Application July 21, 1943,- Serial- No. 495,556

This invention relates generally to fire control systems for use on aircraft, and particularly concerns improvements in computers for aiming guns carried by the craft-at targets either in the form of attacking aircraft or targets located on the ground.

The production of larger aircraft has made it possible to mount correspondingly larger guns thereon and thus increase the effective range of guns carried by the aircraft. More accurate fire control systems have become necessary inorder to utilize the longer range guns to the greatest advantage. One example of an aircraft fire control system of this type is described in copending application Serial No. 411,186, now abandoned, for Inter-Aircraft Gun Sight and Computer, filed September 17, 1941, in the names of Carl G. Holschuh and David Fram.

The present invention may be considered an improvement over that disclosed in the aboveidentified application in that it is particularly adapted for use with a radio sight as well as an optical sight. The present invention is also particularly adapted for use in a stabilized fire control system having a gyro and associated servo mechanisms.

One object of the present invention is to provide an improved computer for fire control apparatus of aircraft.

Another object of this invention is to provide an improved range finder for supplying the range of a target to a computer.

A further object of the invention is to provide a computer for aircraft having an improved mechanism for computing the time of flight of a projectile to a target.

A further object of the invention is to'provide a computer for aircraft having an improved prediction device for determining the futur position of a target.

A further object of the invention is to provide a computer with a conversion mechanism for converting lateral and slant elevation prediction angles to azimuth and elevation prediction angles.

A still further object of the invention is to provide a computer for aircraft with an improved ballistic correction mechanism for accurately determining ballistic correction angles necessary in order to direct a projectile towardthe predicted future position of a target.

Other objects and advantages of the-invention will become apparent from the following specification taken in connection with the accompanying drawings, wherein:

Fig. 1 is a diagramshowing trigonometric rela- 2 Claims. (01. ass-41.5)

tions involved in the fire control problem, which must be solved by an aircraft computer;

2 i a space diagram ShQW th t ig???- metric relations, of the prediction angles to the angles necessary for offsetting the guns relative to a line of sight in ordento direct them toward the predicted future position of the target;

Fig. 3 is a schematic and .block diagram of components of an aircraft fire control system including a computer embodying the present invention;

Figs. 4a and 4b are schematic diagrams which, when taken togethenshow details of the components of the computer shown in Fig. 3;

Fig. 5 is a schematic diagram of a modified form of :the time of flight computing mechanism shown in Fig. 4b;

Fig. 6 is a schematic diagram of a further modified form of time of fiightmechanism shown in Fig. 4b;

Fig. 7 is a modified form of the conversion mechanism shown in Fig. 4b.

Fire control problem Considering first the general problem and theory involved in directing the fire of guns mountedon aircraft, reference is made to Fig. 1 wherein a defending aircraft 1 is carrying guns adapted to be directed by the fire control system. An attacking aircraft 2 approaching the defending craft I is located at. a distance or range (D0) and at an observed angle (00) relative to the longitudinal axis of defending craft l. The attacking craft may be considered as proceeding on a course 3 and having velocity relative to the defending craft Irepresented by a vector V.

Itis possible with either radio or optical sights to determine the'distance (D0) ,of the target or attacking plane 2 .and the angleiflo) of the line of sightfrom the defending craft It thetarget. It is also possible to determine the angular rate of movement of the target 2 relative to the craft l by measuring the rate of change of the angle 00.

This angular rate of change 7 oftheline of sight depends upon the relative velocity (V) ofthe target 2, the range ofthe target (D0), and the angle between the course 3 and the linev of sight. Thi angular rate may be expressed in the following terms:

V cos a (1) D0 wherein V is the rel'ative velocity of the target 2 along,the-.cou-rse 3vand (a) isthe angle between the course 3. andaline perpendicular .to the line of sight as shown in Fig. 1.

resenting the predicted future position of the target. The time of flight necessary to determine this future position depends upon a number of variable factors including the future range (Dp) of the predicted position 6, the indicated air speed of the defending craft I, the altitude of the defending craft I, the angle (p) of line of position relative to the axis of the craft I, as well as certain'constants depending upon the particular type of gun used and the muzzle velocity of the gun.

An exact solution of the predicted future position is quite complex; It has been found that a reasonably accurate approximation ispossible if certain of the variable factors are eliminated and certain assumptions made. From an inspection of Fig. 1,it will be apparent that (V cos (1)7, 2) wherein Tp is the time of flight of the projectile from a gun'on the defending craft I to the predicted future position 6 on the target 2 and Dp is the future range of the target.

Equation 2 may be written as:

sin A:

sin A:

By substituting (0'0) from Equationl me Equation 3 we have:

The futur time of flight (Tp), in the foregoing equation, is. the time, required for a projectile to travel'to the target, that is, a distance equal to the future range (D By determining the time required for a projectile to travel a distance equal to the present range (D0) certain approximations are possible which simplify the solution of the above equation. The time required for a projectile to travel a distance equal to the present range (Do) will hereinafter be referred to as the present time of flight (To). 1

It has been found that in almost all cases the ratio of the present time of flight (To) to the present range (Do) is approximately equal to the ratio of the future time of flight (Tp) to the future range (Dp). By using this approximation and substituting the present time of flight (To) in Equation 4, and further assuming, that for the small prediction angle involved, the prediction angle (A) derived is approximately equal to sin A, the Equation 4 may be rewritten as Although the observed angular rate (0'0) is less than the future angular rate (0 for an incoming target, th present time of flight (To) is greater than the future time of flight (T In this case the true prediction angle (A) depends upon the product of the present angular rate and a time of flight greater than the future time of flight. Since the ratio of the present range to the future range is greater than unity, the error in prediction resulting from assuming the present time of flight equal to the ratio of the present range to future range multiplied by future time of flight is small.

In a similar manner it may be reasoned that Equation 5 is equally accurate for receding targets. Thus, by determining the present time of flight (T0) of a projectile from a gun on the defending aircraft I to the present position of the target 2, it is possible to predict accurately the future position of a target as the product of the observed angular rate (0'0) and the present time of flight (To). Having thus determined the prediction angle (A) it is possible to add this angle to the angle (00) of the line of sight to obtain the angle (0 of the line of position 5 to the future position 6 of the target. It is then necessary to correct for the effect of ballistics on the shell after it leaves the gun in order to determine the gun aiming angle 0%) at which a gun must be positioned to direct a projectile toward the future position 6 of the target.

' In addition to the muzzle velocity (MV) of a gun and certain other gun constants, a projectile leaving the muzzle of a gun is affected b the velocity of the aircraft, wind resistance, and gravity. Thus the projectile is affected by a number of variable factors including the future range (Dp) of the target, the indicated air speed (IAS) of the craft on which the gun is mounted, the

altitude (H) of the craft, and the angular posiaiming angle (0 After the ballistic correction angle (6) has been determined, it may be added to the future position angle (0 of the line of position 5 to obtain the gun aiming angle (1%,) at which the gun must be positioned in order to direct a projectile toward the future position 6. The gun aiming angle (0 may also be expressed as the sum of the observed angle (60) of the target 2, the prediction angle (A) and the ballistic correction angle (5).

This discussion of the theory involved has been confined to a single plane, which is the plane including the gun on the defending craft I and the present and future positions of the target 2. However, equipment used at the present time for aiming guns is movable in lateral and vertical directions about two independent axes, usually referred to as azimuth and elevation movements. It is necessary, therefore, to resolve the angles which have been discussed into lateral and vertical components.

Tracking system A fire control system for aircraft embodying the present invention may be arranged for either automatic or manual operation and used with either radio or optical sighting systems. Referring to Fig. 3, a radio sight is designated generally at I I and includes a scanner mechanism I2 carrying a directional antenna I3 which is connectedin a suitable manner to a radio transmitter I4 and receiver I5 of the ultra high frequency type. The operation of the radio receiver and transmitter does not form a part of the present invention, so a detailed description is believed unnecessary,

Ultra high frequency energy enerated by transmitter I4 is usually radiated by directional antenna I3. Energy reflected by' a target is received by the antenna I3 and supplied to the receiver I5 to which are connected azimuth and elevation phase-sensitive amplifiers I1 and I8,

'Which are of suitable design to, produce electrical responding to the lateral and vertical displacement of the axis of the directional antenna l3 relative to the target.

If the system is to be used for automatic tracking, the switch 2I is closed to the terminals I9. The lateral and vertical error voltages are thus supplied to a gyro unit 23 as by leads 2 1 and 25 to apply torque to the gyro in a manner subsequently described to cause it to process in a direction to follow movements of the target.

When the system is used for manual tracking, the switch 2I is closed to terminals 21 so the torques applied to the gyro unit 23 are controlled by a tracking control handle designated generally at 29. These handgrips are movable about vertical and horizontal axes to eifect corresponding displacement of the line of sight. The tracking control handle is of conventional design which includes grips 3|, that may be rotated about a vertical axis to drive through gearing 32 to rotate a slider 33 of a potentiometer 34 which is mounted on a shaft 35. The terminals of the potentiometer 3 are connected to a battery 36, the midpoint of which is connected as by lead 31 to the midpoint of potentiometer 35. The midpoints of the battery and potentiometer are also connected to ground. In this manner a voltage is produced between a lead 38 connected to the slider 33 and ground, having a polarity and magnitude corresponding to the direction and amount of angular displacement of the hand grips 3! about the vertical axis.

Similarly, movements of the hand grips about the horizontal axis cause a pinion ll to translate a cylindrical rack 12 whereby another cylindrical rack 43 drives a pinion 15, to move a slider 46 of potentiometer 41 which is mounted on a shaft 48. The potentiometer has its terminals connected to a battery 59, the midpoint of which is connected to the midpoint of potentiometer A? and to ground. The voltage between lead connected to the slider 66 and ground has a sense and magnitude corresponding to the direction and amount of the angular displacement of the hand grips 3! about the horizontal axis. The leads 3S and 5! are connected to terminals 21. When the switch 2! is closed to the terminals 21, the leads 38 and 5| are connected to leads 24 and 25 respectively.

Referring now to Fig. ia, the manner in which torques are applied to cause a gyro to precess and track a target will be described. The voltage corresponding to the azimuth signal from either the tracking handle 29 or the radio sight II is supplied by lead 24 to an azimuth torque motor amplifier 55 (Fig. 4a), which is adapted to control the torque applied by a torque motor 56 to a horizontal axis 5? of the gyro designated generally at 58.

The gyro includes a main supporting shaft 6|, which carries a bracket 62 for movement about a vertical axis 63. A housing or follow-up member 65 is supported in the bracket 62 by horizontal trunnions 64, 64, which also support gimbal ring 65- A gyro rotor 61 having a spin axis 68 is pivotally supported for movement about the vertical axis 63 within the gimbal ring 55. A ring H is supported by trunnions I2 and i3 in the housing 65 for movement about the vertical axis 63. A shaft I4 connected to the rotor G? and coincident with the spin axis 68 thereof is restrained in a slot 15 to move the ring H as the rotor 61 moves about the vertical axis 63." The torque motor 56, and a similar torque motor :16 for applying torque :about the vertical axis 63, are both= carried by'the housing 65.

Torque applied by the-motor 56 about thehorizontal'axisfil is transmitted by gimbal. ring 66 and trunnions 8| and 82 to the rotor 61, causing it to precess about the vertical axis 63. Similarly, torque applied to the rotor 6'! about the vertical axis 63 is transmitted by ring H and shaft M,

causing the rotor 63 to precess about the horizontal axis 51.

A pick-01f such as E-transformer 93is carried by the housing65 andhas a-movable armature-8:5 mounted onthe ring it. Movement of the rotor 6'1 about the vertical axis 63 produces a reversible phase, variable magnitude voltage in the output of the coils of pick-off 23 corresponding to thedirection and amount of the displacement of the armature 86 relative to the pick-oft 33. Pick-off transformers of the kind referred to are well-known devices and suitable ones are disclosed in PatentNo. 2,407,657 to O. E. Esval, issued September 17, 1946, and Patent No. 2,412,614 to R. Haskins, Jr., et al., issued Dec. 17,1946. 1

A similar pick-ofi or E transformer 86, also carried by the housing 65, has a movable armature'BIon the gimbal ring 66 whereby a reversible phase, variable magnitude voltage is produced-at leads 88 corresponding to the direction and amount of the displacement of thearmature 81 relative to the transformer 86. Thus signals-are produced at leads 85 and 88 corresponding to movements of the rotor 61 about thevertical axis 63 and the'horizontal axis 5 respectively. The signals produced at leads 85 are supplied to an amplifier 91 which controls a servomotor- 92 to move the housing in a manner to follow mcvenients of the ring II. Similarly, the voltage at leads 88 is supplied to an amplifier 93 which-controls a servomotor 94 to move the housing--65 about the horizontal aXis 5! to follow-movements of the gimbal ring 66.

The amplifier 9| includes a transformer 95 by which the voltage of leads 85 is applied in phase opposition to phase detecting tubes 96 and 91 which are arranged'in a conventional phase detector circuit, having a reference voltage from a source 98 applied through transformer 99in like phase to the two tubes.

When the armature 84 is centered relative'to the transformer 83, no error signal is produced at leads 85. In this case equal voltages appear across load resistors IOI and I62 of the phase detector circuit. Displacement of the armature 84 introduces an error voltage which adds to the reference voltage in the circuit of one of the tubes I06 or Ill! and subtracts in the circuit of the other tube. Thus, the, voltage across one of the load resistors II or I flz increases while the other decreases depending. upon the phase of the error voltage,'as'determined bythe direction of the displacement of armature M. The difference be tween the voltages across the load resistors lei and I02 corresponds to the amount of the displacement of the armature 64 relative to the transformer 83.

The voltage across load resistors I0! and N12 is applied through suitable diiferentiating networks I03 and I04 to the grids of amplifying tubes I96 and I01. A source of positive Voltage such as battery I08 is connected to the. plates of the amplifying tubes I06, and I0! through windings'I09 and II I of the servomotor 92. The currents through windings I69 and III dependupon the voltage applied to grids I06 and. I91. Since the difference between the grid voltages corresponds to the direction and amount of the displacement between armature 84 and transformer 83, the motor is rotated in a direction and at a speed corresponding to the direction and amount of said displacement. Motor 92 drives through shaft H2 and gearing H3 to rotate the shaft carrying the bracket 62 and thus positions the gyro housing 85 about vertical axis 63. When the housing 65 is so positioned that the armature 84 is centered relative to the core of transformer 83, the voltage between leads 85 is zero, so the motor 92 develops no torque and therefore does not rotate.

The differentiating or rate networks I03 and I04 produce derivative signals which aid the stabilization of the servo system.

The shaft H2 also drives through gearing H4 to position the rotor of a suitable self -synchronous transmitter I I0 that is energized by a source I20.

cable I00 having a phase relation with the source I corresponding to the angular displacement of the transmitter H0. Transmitter H0 may be of any conventional design such as Selsyn,f Autosyn, or Telegon mechanism I (Fig. 3) to position the scanner I2 in accordance with the azimuth position of the gyro housing 65. v

The amplifier 93 controls servomotor 94 in a similar manner as the amplifier 9I controls servomotor 92. The voltage from leads 88 is compared in phase with a reference voltage from source H5 by a phase detecting circuit including tubes H6 and H1. The output voltage of tubes H6 and H1 is applied to the grids of amplifying tubes I I8 and I I9, which can control the current in windings I2I and I22 of the motor 94. In this manner the direction and speedof rotation of shaft I21 correspond to the direction and amount of the displacement of the armature 81 relative to the core of transformer 86.

The shaft I21 forms one input of a compensating differential I28, the other'input of which is driven from gearing I I3 whereby output gear I29 drives through gears I3I, shaft I32, and gearing I33 to rotate shaft I34. The shaft I34 in turn drives through gearing I35 to position shaft 64 and the housing 65 about the horizontal axis 51. Thus the pick-off 86 and amplifier 93 control the servomotor 94 to cause the housing 65 to follow movements of the gyro rotor 61 about the horizontal axis 51'. The compensating differential is used in a conventional manner to avoid undesired movement of the gyro housing about the horizontal axis 51 upon rotation of the housing about the vertical axis =63.

The shaft I21 also drives through gearing I38 to position the rotor of a position transmitter I39 that is energized from a source I4I. Output leads I 42 from the transmitter I39 carry a voltage displaced in phase in accordance with the direction of rotation of the shaft I21. This voltage controls an elevation servo mechanism I43 (Fig. 3) to position the scanner I2 in elevation to correspond with the elevation position of. the gyro rotor 61,

Since the scanner I2 follows movements of the rotor 61, the gyro acts as a stabilizer so the scanner is stabilized in space. r 7

In addition to the radio sight, the system also includes an optical sight designated generally at !5I and including a sighting prism I52 arranged to be rotated in elevation about a horizontal axis 1 We w we and sector '54- r lpfism .1

.20 The transmitter supplies a voltage by leads in .25 to control a servo adjusted in azimuth about a vertical axis by gearing I55 in any suitable well-known manner. The voltages appearing on leads I00 and I42 also control suitable servo mechanisms I51 and I58 to position the sighting prism I52 in azimuth and elevation in accordance with the position of the gyro rotor 61, thereby stabilizing the optical sight in the same manner as the scanner I2. The image of a target is reflected by the prism I52 through adjustable stadia lines I63 arranged to be moved in opposite directions by a lead screw I64 to determine the range of an object, as will subsequently be described. The image is then reflected by reflector I65 to an eye-piece I8I.

When the switch 2I is closed to the terminals 21 for manual tracking, voltages are supplied through leads 24 and 25 to azimuth and elevation torque motor amplifiers 55 and HI respectively. A voltage from the potentiometer slider 33 corresponding to the azimuth position of hand grips 3| is supplied by lead 24 to grid I13 of tube I14 which includes a cathode I15 and a plate I15 connected in a differential amplifier circuit including tube I85. Positive voltage is supplied to the plate I16 from a source such as battery I11 through load resistor I19. A negative voltage is supplied from a battery I19 through a common cathode resistor I8I to the cathode I11.

Suitable bias is provided for the grid I13 by a battery I83 connected through a grid-leak resistor I84 to the grid I13. A second tube I85 has its plate connected to battery I11 through a load resistor I88 and its grid I connected to bias battery I83 through resistor I81. The circuit of cathode I88 is connected through cathode resistor I8I and the battery I19 to ground.

If no signal is received by lead 24, equal currents are drawn by tubes I14 and I85, and the grids I13 and I80 are at the same potential.

The current normally drawn b the tubes I14 and I is determined by the value of common cathode resistor I8I and the battery I19. It will be apparent that the current increases until the drop across resistor I8I offsets the voltage of battery I19.

Similarly, the voltages across the load resistors I19 and I96 are equal, so equal voltages are applied through resistors I9I and I92 to grids I93 and I94 of amplifier tubes I95 and I95. Cathodes I91 and I98 of the amplifying tubes I95 and I96 are connected through cathode resistors I99 and 20I to ground. A negative bias is supplied from a source such as battery 202 through resistors 203 and 204 to the grids I93 and I94. A source of positive voltage, such as battery 205, is connected through the mid-point of winding 206 of the torque motor 56 to plates 201 and 208 of the tubes I95 and I96. With equal voltages on the grids I93 and I94, currents through the two tubes I95 and I96 and the two halves of winding 206 are equal so no torque is applied to the horizontal axis 51 by the motor 56.

If a positive voltage is applied by the lead 24 to the grid I13, current in the tube I14 and the drop across load resistor I18 increase, as does the current through common cathode resistor I8I. This increase in current through common cathode resistor I8I raises the cathode voltage, thereby making the grid-cathode voltage more negative and reducing the current drawn by tube I85 as well as the voltage drop across load resistor I86. The voltage differential across resistors I18 and I86 is thus applied to grids I93 and I94, thereby changing the currents through the tubes I95 and I96, and the two halves of winding 2l16.

The diirerence in the current in the two halves of winding 206 causes torque motor 56 to apply torque to horizontal axis 57. The torque applied has a direction and magnitude corresponding to the polarity and magnitude of the voltage appearing at lead 24. Thus, if the voltage of the lead 24 is negative instead of positive, torque motor 56 will apply torque in an opposite direction.

Similarly, the elevation control voltage of lead 25 is applied to the grid of tube 2| I which is connected in a difierential amplifier circuit with tube 2 I2. Due to the action of common cathode resistor 2I3, the signal of lead 25 causes the current drawn by one of the tubes to increase whereas that drawn by the other decreases, and the voltage across their corresponding load resistors 2M and 2I5 changes in opposite directions. This change in the voltage across load resistors is amplified by tubes 2I'I and 2I8 having calibrated cathode resistors 2I9 and 22I to control the current through the two halves of winding 222 of the torque motor I8. The torque applied by the motor 18 about the vertical axis is controlled in this manner so it corresponds in direction and magnitude to the polarity and magnitude of the voltage applied by lead 25.

It is a characteristic of gyroscopes that, when a torque is applied about one axis, the gyro rotor processes about a second axis at a rate proportional to the torque applied. Since the torque applied by the torque motors 56 and I8 depends upon the difference between the currents in the two halves of the windings 2'56 and 222, signals proportional to these current differences will also be proportional to the torque applied. In the case ofthe torque motor 56, the currents drawn by tubes I95 and I96 correspond to the diiierence in the currents through the two halves of the winding 206. The voltages across calibrated cathode resistors I99 and 20I have a voltage differential proportional to the torque applied by the motor 56 and corresponds to the-azimuth precession rate of the gyro rotor 67 about the vertical axis 63. These voltages are connected by leads 22-5 and 226 across potentiometers 221 and 228 of a prediction mechanism 229.

In a similar manner the difference in the voltages across resistors 2I9 and 22! in the cathode circuits of tubes H8 and 2I9 is proportional to the torque applied by the motor 18 about the vertical axis 63 and corresponds to the elevationprecession rate of the gyro rotor 67. These voltages are connected by leads 23I and 232 across potentiometers 233 and 234 of the prediction mechanism 229.

As will be described m detailsubsequently, the angular rates represented by the voltages of leads 225 and 226 correspond to the precession rate of the gyro in a lateral plane including the spin axis 68. The elevation rate, represented by leads 23I and 232,. corresponds to the elevation precession rate of the gyro rotor 67 in a vertical plane perpendicular to the lateral plane and also including the spin axis 68.

When the switch 2| is closed to terminals I9 representing the automatic tracking position, the voltages from the azimuth and elevation phase sensitive amplifiers I1- and I8 are applied by leads 24 and 25 to the amplifiers 55 and Ill, respectively, to cause the gyro rotor 6! to process to follow movements of the target. In this manner, the spin axis of the gyro is maintained coincident with the line of sight to the target.

thus automatically track the target.

Range computer unit In addition to data corresponding to the angular position of the target, the computer must be supplied with data corresponding to the range of the target.

The range may be determined optionally with the radio-sight or the optical sight, depending upon prevailing conditions of visibility, and so forth. In the case of the radio sight, the range 1 is determined automatically by a known apparatus which is not a part of the present invention. When determining the range by using the opticalsight, knob 263 is adjusted with reference to a scale (not shown) to set in the dimensions of the target and the operator controls the position v puter unit 25 I of a foot pedal 2M (Fig. 3) which, as will ap pear, controls the rate of motion of stadia lines I63 which are positioned to just bracket the target. In doing so, the range foot pedal 2M controls the position of a slider 242 on potentiometer 243, the terminals of which are connected to a battery 244 having its center-point grounded. When the operator is accurately tracking the target, the voltage of slider 242 is proportional to range rate (D and has a positive or negative polarity, depending on whether the range is decreasing or increasing as the target approaches or recedes from the defending craft. The method of .measuring range by adjusting stadia lines to bracket a target of known dimensions is well known.

245 and condenser 246 to a terminal 241 of a switch 228. The diiierentiating network produces a rate signal which anticipates changes and assists the operator in tracking. When the switch 248 is closed to the terminal 241, the range rate voltage is supplied to a rangecom- The range computer unit 251 produces a voltage proportional to range (D0) in a manner to be described.

This voltage proportional to range is supplied by a lead 336 to grid 252 of amplifying tube 253,

which has a resistor 254 connected between cath- -the voltage of lead 256 equal to zero when the voltage on grid 252 iszero, a negative voltage from a source 251 is connected through a resistor 260 and resistor 254 to the cathode 255. The values of the resistances are so chosen that the lead 256 is at ground potential when there is zero voltage applied to the grid 252. Since the voltage applied to grid 252' corresponds to the range (D0) of the object, an amplified voltage proportional to the range (Do) appears at lead 256 and. is applied across potentiometer 258. A slider 259 for the potentiometer 258 is positioned by a shaft 26I according to the position of the stadia lines I63.

It is well known that in conventional stadio metric range finders the ratio of the distance (d) between stadia lines to the focal length (1) of the optical system from the stadia lines to the focal point is equal to the ratio of the dimensions of the target (TD) to the-total range 11 (Do). The dimensions of the wing spread of enemy airplanes is known to the gunners operating the apparatus.

The present range computer is based upon this principle and is desi gned to equate the target dimensions (TD) to the product of the distance (d) between the stadia lines and the total range (Do) divided by the focal distance (1) from the stadia lines. A voltage proportional to the target dimensions (TD) is set into the mechanism by rotation of a handwheel, 263, with reference to a target dimension scale, not shown. This hand wheel is arranged to position slider 264 of potentiometer 265, the terminals of which are connected to a battery 296. The voltage at the slider 264 is proportional to the target dimensions and is applied to grid 261 of tube 268. Cathode 269 of tube 268 is connected to cathode 21I of tube 212, which has its grid 213 connected to the slider 259 of potentiometer 258. Plates 215 and 216 of tubes 268 and 212 are supplied with positive voltage from a source such as battery 211, which is connected to the midpoint of winding 218 of motor 219.

It is desirable, in order to properly control the motor 219, for certain currents to be flowing through the tubes 268 and 212 at all times. This is accomplished by applying a negative voltage from ground to the cathodes 269 and 21I as by battery 210, which is connected through a resistor 214 to the cathodes 269 and 21I. With this arrangement a normal current flows through tubes 268 and 212 until the drop across resistor 214 ofisets the negative voltage of battery 210.

The motor 219 drives through gears 28I and 282 to rotate lead screw I64 and thereby position stadia lines I63 so that they just enclose the target. The position of the stadia lines I63 determines the distance (d) between them. Since the focal distance (I) from the stadia lines is substantially constant, the quotient 11/) of the distance (d) divided by the distance to the focal point may be determined by the ratio of a gear 284 to the gear 282 whereby the shaft 26I is rotated in accordance with this quotient. As hasbeen previously explained, a voltage proportional to range (Do) is supplied to the potentiometer 258. Since the slider 259 is rotated in accordance with the quotient (oi/f), the voltage appearing at the slider 259 is propotional to the expression dXDo f This voltage is applied to grid 213, whereupon different currents flow through the two halves of winding 218 of the motor 219, thereby causing the motor to rotate in one direction or another, depending upon which of the currents is larger. The rotor 219 therefore adjusts the stadia lines I63 until the voltage applied to the grid 213 is equal to the voltage applied to grid 261. This, of course, is dependent upon the voltage applied to the grid 252 of the tube 253, which, as has been explained, is proportional to the range (Do) and depends in turn upon the position of slider 242 which is adjusted by the range foot pedal 24I.

The voltage from switch 248 is supplied to the range computer by a lead 29I, which is connected to grid 292 (Fig. 4b) of a tube 293, that is arranged in a balanced amplifier circuit similar to that of the tubes 268 and 212 which control the motor 219. The tube 293, together with tube 294, controls range servomotor 295, having a shaft 296 which is adapted to drive a logarithmic --1z a function of the range (Do) into mechanism. Shaft'296 drives through gear 291 and shaft 298 and gear 299 to positionan antilogarithmic cam disc 30I. having a groove 302 designed to position sector follower racks 303 and 304 and thereby rotate pinions 305 and 306. Since the cam disc SM is rotated in accordance with the logarithmic function of the range (Do), the pinion 305 is rotated in accordance with range (D0) and drives through a shaft 309 to position a slider 301 of potentiometer 308 in accordance with range (Do) The potentiometer is supplied with av voltage by lead 309 corresponding to'the voltage output of a permanent-magnet generator 3II, which is driven by the range motor 295 through gearing 3I2. The voltage output of the permanentmagnet generator 3 represents thedifferential of the output of range motor 295. Since the output of range motor 295 as represented by shaft 296 is proportional to logarithmic function of the range (Do), the differential of this is the quotient of range rate (D divided by range (Do). This voltage is supplied by the lead 309 to potentiometer 308 where it is multiplied by the value of range (Do) as determined by the position of slider 301. This provides a voltage proportional to range rate (D which is applied to grid 3I3 of the tube 294.

Plates 3I4 and 3I5 of the tubes 293 and 294 are supplied from a suitable source such as battery 3I6 connected to the mid-point of winding 3I1 of the range motor 295. 'It will be apparentthat the currents in the two sides of winding 3I1 will be unequal when unequal voltages are applied to the grids 292 and 3I3. This causes the range motor 295 to rotate in a direction which adjusts the slider 301 of potentiometer 308 until the voltage of the grid 3I3 is equal to the voltage of the grid 292. Cathodes 358 and 3I9 of the tubes 293 and 294 are connectedthrough a resistor 32I to a source of negative voltage such as battery 322. This negative voltage causes normal current to flow through the two tubes until the drop across resistor 32I offsets the negative voltage of the battery. This is done in order to have a minimum current through both halves of the winding 3I1 to provide a more accurate control of the motor 295.

As has been explained, the sector rack 304 is moved by the anti-logarithmic cam disc 30I to rotate the pinion 306. The gear ratio of pinion 306 is selected in a manner to divide the range (Do) as determined by the rack 304 by a value of the muzzle velocity (MV) of the guns being used with the computer. This is done to provide a portion of the time of .flight solution, which will hereinafter be described in more detail. The pinion 306 drives through gearing 325, shaft 326, and gearing 321 to rotate a spur gear 328 which meshes with a pinion 329 to position slider 33I of the potentiometer 332. The ratio of pinion 329 to spur gear 328 is arranged to eliminate the muzzle velocity factor which was introduced by the pinion 306. Hence, the slider 33I is positioned in accordance with the range (Do). The terminals of potentiometer 332 are connected to a voltage source such as battery 333. The voltage of the slider 33I is proportional to the range of the target and is supplied by lead 334 to the grid 252 (Fig. 3) of tube 253 for controlling the motor 218 as heretofore described.

The range computer thus far described has been for use with the optical range finder which is qrit q c y t e range too pedal 24L While the computing the optical rangefinder is in-use, theswitchddfli is closed to the terminal 241' and switch 335. When.

(Fig. 4b) is closed to the terminal 336. the automatic radio range computer 341' of thev radiosight H is used, the range computer. 2.5].

isused in a slightly diiferent fashion. Switch 248 is closed to terminal 342, which represents ent invention) which is adjusted to measurethetime interval between the transmission of a pulse of high frequencyenergy by the antenna I3 and the reception of a reflected pulse of energy-by. the antenna. In the system illustrated, the phase shifting network includes a rheostat 344 which is connected to the automatic radio range finder 3 (Fig. 3) by leads of a cable 345. A slider 346 on the rheost'at 3 34 is positioned: in accordance. with the range (Do) as determined'by. the. pinion- 365 whichdrives through gears 36!.

The position of the slider 348. on the rheostat' 344 acts to determine the phase shift effected by the phase shifting network of the automatic radio range finder 3M A range error signal is supplied fromthe radio range finder 34! by a lead 35! to the terminal 342 of the switch 248. This range error signal is now connected by lead 291 to the grid 292 (Fig. 4b) of the tube 293. Since the switchr335 is closed to terminal 3%3, the signal output of. the permanent-magnet generator 3.! l. is connected to the grid 353 of the tube 2-94 through a suitable differentiating network composed of resistor 353 and condenser 354. Thus, a voltage appearsacross. resistor 355, which is proportional to the output of the permanent-magnet generator 31 I, that is, the rate of change of the outputof the range motor 295. Since the voltage now supplied to the grid 292 is an error signal, the range motor 295 will drive through the anti-logarithmic cam disc 36! until the phase shift as determined by potentiometer 344 represents thecorrect value of range measured by the automatic range finder 34!. When this occurs, the error signal of lead 351 is zero. The voltages applied to the grids 292 and 313 are both zero since the range motor 295 and the generator 3!! stoprotating.

From this description of the range computing. unit 25!, it will be apparent that the output shaft 296 of the motor 295 drives a logarithmic; function of range (D) into the computer. The logarithmic function just mentioned, and other functions referred to herein are determined bygraphic procedure from ballistic tables. supplied by the government. The method of deriving desired functions is well-known to those skilled in the art. Since such functions vardy in accordance with the geometric and dynamiccharacteristics of different kinds of projectiles, no specific functions are mentioned herein.

The range computing unit 2 also includes amp-- paratus for supplying a range rate (13 which is represented by the rotation of shaft 851-, that is driven by range rate motor 352. This range rate motor is controlled by a balanced amplifier circuit including tubes 363 and 354, the plates of which are connected through opposite halves of winding 385 to a source of positive potential such as battery 365. Grid 35'! of the tube 364 is supplied with a voltage from a slider 30.! of potentiometer 388 corresponding to range rate (1 30) as has already been described. The range 14-? ratea motor rotates; and drives through gearing, 369 to position; slider 37 lof; potentiometer 312.- Theterminals of' the-potentiometer 312 are connectedqto a battery3l3, themidpoint of which isconnected to; ground A voltage having a polarity and magnitude corresponding to range rate is applied from slider 3' to grid 315 of tube 363 so the-- rangeprate motor: 362 rotates. until the voltage of slider 3:11 is equal to the range rate voltage applied; to; grid; 36]. A suitable source of'negativepotential, such as battery 3T1, is connected. throughresistor- 318; to cathodes of tubes23153; and 354'; in, order to provide a; certain. normalcurrent through the winding 365. of the motor.- 362;

It". willpbe apparent that the shaft 3,6l of range rate.motor-fifizarotates inaccordance with 1 a functionof range rate (D The motor shaft 36l drives. through gearing 3.19;; to rotate shaft 3Bl in accordance with the function of range rate (Do).

Time, 0 f flight unit In' order. to predictthe future position of a target; it. is necessary. to determine the time of flightof a projectile :fromguns on the defending craft to=the ObSEIVBdaPOSitiOIl of thetarget. As has beenexplained; the present time of flight (To) may be combined. with; angular rates; of movement of an attacking craft ortarget to determine a prediction: angle (A).

The present time: of: flight-depends upon many factors. In order to reduce errors in computation of time of flight (To), the calculation may .be divided into. twoparts, namely, that part which;- represents the. time of. flight a vacuum (Tt), which isapprox-imately; a linear function ofi range, (Do), and: that part which depends upon the other. variable functions. The latter part, which is hereinafter referred; to as the difference in the time of flight (AT0), is also a function of range-,. but in addition. includes functions of the altitude and air; speed. of the target as; well as functions of the, gun position angles. Three time-of-fiight' mechanisms are described herein; however; the preferred and simplified form is that: shown in Fig. 412. as; a component part of the computer. However, the other forms, which will: be hereinaft r d sc ibed ma be e curate under certain circumstances and may be used in the computer if desired. It has been found by experiment that the future range, the azimuth; position of the guns of the defending craft, and the altitude of the craft have the greatest. effect upon the time of flight. Since the. airspeed usually varies between comparatively small limits during normal flight, an average value. of airspeed may be used. Similarly, an average Val e. Of the elevation angle of the guns. m y-beused;

Since, it is; desired to determine the present time of flight (To), it is possible to substitute the observed; azimuth (A0) of the target for the azimuth position of the gun (Ag) since the only difference between these angles would be the azimuth ballistic correction angle. This is sufli ciently small that itdoes not materially affect timewf-flight computations. I

The time of flight (TV) of the projectile in vacuum is determined by the shaft 326 which, as was; explained in connection with the range computer, is rotated in accordance with. the quotient of the range (Do). divided by the muzzle velocity (MV) of the guns. This value of Tv is supplied by shaft 326; directly to the time of flight unit 385 (Fig. 3). The logarithmic function. of range (Do) represented by shaft 296 is also supplied to the time of flight unit 385. The observed azimuth (A) position of the target is supplied by the shaft N2 of the gyro unit 23 through gearing 389 and shaft 428 (Fig. 3) to the time of flight unit 385.

The only other function necessary to operate the time of flight unit 385 is the function of altitude. A handwheel or knob 388, which may be positioned at a remote point from the computer such as the pilots or navigators compartment, is adjusted on a logarithmically calibrated scale to rotate shaft 389 and winding 39! of a self-synchronous transmitter 392, such as a Selsyn or Telegon, in accordance with a logarithmic function of altitude (H). The

winding 39! is energized from a suitable source 393 and induces voltage in stator winding 394;

The stator 394 is connected to a stator 395 of a self-synchronous receiver 396 having its rotor 391 connected to the primary 398 of a coupling transformer which has split secondary windings 399 and 40L The voltage of primary 398 is applied in phase opposition to plates of phase detecting tubes 402 and 403. The voltage of a source 404 which is synchronized with the source 393 is supplied by transformer 405 in like phase to the plates of the tubes 402 and 403. This is a conventional phase detecting circuit in which the differences of the direct current voltages appearing across resistors 406 and 401 in the circuit of tubes 402 and 403 correspond to the direction and amount of the displacement of the receiver rotor 391 relative to the transmitter rotor 391. These difference voltages are connected through condenser and resistor differentiating networks 408 and 409 to amplifying tubes 41! and M2, having the two halves of winding 4I3 of altitude servo motor 414 in their anode circuits.

The motor 4l4 drives through worm gear M5 and Worm wheel M6 to position shaft 4l1 which drives through gearing M8 to position shaft M9. The rotor 391 is positioned by the shaft 4l9 until the position of the receiver rotor 391 corresponds to the position of transmitter rotor 39l. When this occurs, the voltages across resistors 406 and 401 are equal, and the motor 414 is stationary since the currents in the two halves of the winding 4l3 as determined by amplifying tubes 4 and 4| 2 are equal.

When an equilibrium position is reached, the position of shaft 4l9 corresponds to the position of the shaft 389 and handwheel 388; hence, shaft 4 l 9 is positioned in accordance with a logarithmic function of altitude (H).

Shaft 4|9 drives this function of altitude through gearing 42l, shaft 422, and gearing 423 to position shaft 424, which drives the logarithmic function of altitude (H) into the time of flight unit 385.

The difference in time (AT0), which must be combined with the time of flight in a vacuum (Tv) to determine the present time of flight (To) is a function of the product of the three variable functions, as has heretofore been described. These variable functions are functions of range (Do) altitude (H), and azimuth (A0) The product of these three functions may be easily obtained by adding their logarithms. Logarithmic functions of range (D0) and altitude (H) are introduced into the time of flight unit 385 by shafts 296 and 424.

The observed azimuth (A0) of the target is iables into the time of flight mechanism.

driven through'shaft H2 (Fig. 4b), gearing 425, shaft 426, and gearing 421 to rotate shaft H2, which drives through gearing 386 to rotate shaft 428 in accordance with the observed azimuth (A0) position of the target. The shaft 428 drives through pinion 429 to position a logarithmic cam disc 43! having a cam groove 432, which positions a sector rack 433 in accordance with the logarithmic function of the azimuth position of the target (A0). The sector rack 433 drives through pinion 434, shaft 435, gearing 436 to position shaft 431, which represents one input of a differential 438.

The logarithmic functions of range (D0) and altitude (H) as represented by rotation of shaft 296 and 424 are added in differential 431 having output shaft I which drives a second input of the differential 438. It will be apparent that the shaft 44! is positioned in accordance with the sum of the logarithms of range (Do) and altitude (H). The differential 438 adds the logarithmic function of azimuth (A0) to these two functions and positions output shaft 442 in accordance with the sum of the three logarithmic functions. The

.shaft 442 drives through pinion 443 to position an anti-logarithmic cam disc 444 having a cam groove 445 which moves a sector rack 446 to rotate pinion 441.

Since the input to the anti-logarithmic cam disc is the sum of the logarithms of functions of range (D0), altitude (H) and observed azimuth (A0) the output of the anti-logarithmic cam 444 moves gear sector 446 to rotate pinion 441 on shaft 448 according to the product of these three functions. The shaft 448, representing one input of a differential 449, is thus positioned in accordance with the value of the difference in time of flight (AT0). This difference in time of flight (AT0) is combined with the time of flight in a vacuum (Tv) as represented by shaft 326, which also drives an input of the differential 449. The output of the differential 449 as represented by shaft 45I is thus positioned in accordance with the time of flight (T0) of a projectile to the target.

The rotation of shaft 45I representing the time of flight (To) drives through gear 452, shaft 453, and gearing 454 (Figs. 3 and 4a) to rotate shaft 455 to drive the time of flight (To) into the prediction unit 22 9.

This form of time of flight mechanism is the simplest and preferred form since it provides sufficient accuracy for use in the computer being described. However, the accuracy of the result is increased by the introduction of additional var- Figs. 5 and 6, showing modified form of the time of flight mechanism, include additional variables.

Fig. 5 illustrates a time of flight mechanism which utilizes five variables for determining the time of flight (To) These variables include range '(Do) altitude (H), indicated air speed (IAS), gun azimuth (Ag), and gun elevation (Eg). In these mechanisms that portion or component of the time of flight, which is a linear function of range, is computed separately from that portion of the time of flight, which is a variable function depending upon the effect of various forces on the projectile. The time of flight in a vacuum (Tv), which is a linear function of range, may be determined by rotation of shaft 46I which drives into a differential 462.

The change in time of flight (AT0) which must be added to the time of flight in a vacuum (Tv), hasbeen found to be the product of a function of range (Do) and a function of altitude (H),

17 that is raised to power corresponding to a function of the gun position angles, namely, azimuth (Ag) and. elevation (Eg) which is in turn raised to a power which is a function of indicated air speed (IAS).

The gun position angles (Ag and Eg) are introduced by shafts 463 and 484, which rotate and translate a cam 465, the surface of which is such that the lift of a follower 458 riding thereon represents a logarithmic function of gun azimuth and elevation angles. This logarithmic function of gun azimuth and elevation angles is raised to a power which is a function of indicated air speed by translating a three-dimensional cam 481 by in accordance with the product of a function of indicated air speed and the logarithmic function 'of gun azimuth and elevation. The follower 489 includes a rack 411 which drives through pinion 412, shaft 413, and gearing 414 to rotate a shaft 415 representing one input of differential 418.

In order to raise the funtion of altitude to the power of the function of gun azimuth and elevation angles, which is in turn raised to a power of indicated air speed, it is necessary to add the double logarithmic functions of altitude to the product of indicated air speed and the logarithmic function of gun azimuth and elevation angles. A shaft 418 is rotated in accordance with a double logarithmic function of altitude by a pinion 458 which meshes with a rack follower 451 that rides on the surface of a logarithmic cam 458. The cam 458 is driven by a shaft 459 in accordance with a logarithmic function of altitude (H) which may be driven from the shaft 424 of the computing mechanism heretofore described. Since the shaft 459 is driven in accordance with a logarithmic function of the altitude (H), the follower 451 drives shaft 418 in accordance with a double logarithmic function of the altitude (H) The shaft 418 drives this double logarithmic function into the differential 416 where it is combined with the rotation of shaft 415. The output of the differential 416 drives shaft 419, which rotates an anti-logarithmic cam 48L having a follower 482 riding on the surface thereof which is displaced in accordance with the product of the logarithmic function of altitude and a function of azimuth and elevation angles raised to a power of indicated air speed.

This product acts through a rack 483 on the lift 482 to rotate pinion 484 and shaft 485, which represents one input of a differential 485. The other input of differential 486 is driven in accordance with logarithmic function of range (Do) by a shaft 481. The shaft 46!, which is positioned in accordance with range, rotates a logarithmic cam 488 having a follower 489 which is displaced in accordance with a logarithmic function of range and acts through rack 49! and pinion 492 to position the shaft 481. The output of the differential 485 as represented by shaft 493 is the sum of the logarithmic function of range (D) and the product the logarithmic function of altitude (H) and gun azimuth and elevation angles (Ag and Eg) raised to the power of indicated air Speed and logarithmic function of altitude (H). Shaft 493 positions a second anti-logarithmic cam 494 having a follower 495 riding on its surface, which is positioned in accordance with the the product of functions of range and altitude, the function of altitude being raised to a power corresponding to the sum of gun azimuth and elevation angles (Ag and Eg), whichfunction is in turn raised to a power of indicated air speed.

The follower 495 includes a rack 495 which drives pinion 49? to rotate a shaft 489, which represents the change in time of flight (AT0), which must be added to the time of flight in a vacuum (Tv) toobtain the time of flight (T0) of a projectile to the target. The addition of the time of flight in a vacuum (Tv) and the change in time of flight (AT0) is accomplished by the differential 452, the output of which drives shaft 499 in accordance with the time of flight (To).

Fig. 6 shows a still further modification of the time of flight mechani m, which is an intermediate form in that it uses four of the five variables in Fig. 5. The mechanism shown in Fig. 6 is substantially the same as that in Fig. 5 except an average value of gun elevation is used. In this case gun azimuth (Ag) is introduced by shaft 59!, which rotates a three-dimensional cam 582, and the indicated air speed is introduced by shaft 593 which translates the cam 582 whereby a follower 554 riding on the surface of the cam is positioned in accordance with the product of indicated air speed and a logarithmic function of gun azimuth (Ag) The follower 584 acts through rack 595 and pinion 595 to drive shaft 581, representing one input of differential 588. The other input of the differential 588 is driven by shaft 509 that is positioned in accordance with double logarithmic function of altitude in the same manner as the shaft 418 shown in Fig. 5. Thus, shaft 459, which is rotated in accordance with a logarithmic function of the altitude (H), drives logarithmic cam 458, whereby rack follower 451 has a lift corresponding to the double logarithmic function of the altitude (H) and drives through pinion 455 to rotate the shaft 589 in accordance with said double logarithmic function.

The inputs represented by shafts 581 and 589 are combined by the differential 588 to rotate output shaft 51!, which drives through pinion 5l2 to position an anti-logarithmic cam disc 5l3 having a cam groove 514 which positions a sector rack 555. A pinion 5l5 meshes with the sector rack 515 and rotates shaft 5 i 1 in accordance with the product of a logarithmic function of altitude (H) and a function of gun azimuth (Ag) raised to a power of indicated air speed (IAS) The range (Do) is introduced into the mechanism by shaft 5! 9, which drives one input of differential 52! in accordance with the time of flight in a vacuum (Tv) which is a linear function of range (D0). Shaft 519 also rotates logarithmic cam 522 having a follower 523 riding on its surface and positioned in accordance with a logarithmic function of range. The follower 523 drives through rack 524 and pinion 525 to rotate a shaft 525. Shafts 5!! and 528 represent an input of differential 521, the output of which drives a shaft 528 in accordance with the sum of the logarithmic function of range (D0) and the logarithmic function of altitude (H) multiplied by a function of gun azimuth (Ag) raised to a power corresponding to a function of indicated air speed. The shaft 528 drives through pinion 529 to position an anti-logarithmic cam disc 53! and cam groove 532, which positions a sector rack The rack 533 drives a pinion 534 which rotates shaft 535 that is in turn positioned in accordance with the product of function of range (D) and a function of altitude (I-I) which latter function is raised to a power corresponding to a function of gun azimuth (Ag) that is in turn raised to a power corresponding to a function of indicated air speed (IAS) The shaft 535 is therefore positioned in accordance with the change in time of flight (AT0) which is combined with the time of flight in a vacuum (Tv) represented by shaft 535 in differential 52! to position output shaft 536 in accordance with the time of flight (To).

The functions of indicated air speed for the two mechanisms shown in Figs. and 6 may also be obtained from the computer as will subsequently appear in connection with the ballistics unit. The gun elevation function may be supplied from the gyro unit by shaft I21, which has already been described as being positioned in accordance with the observed elevation angle. The difference between the observed elevation and the gun elevation is so small as to be immaterial for purposes of this computer.

Prediction unit A prediction unit 229 includes four potentiometers, 221, 228, 233, and 234 (Fig. 4a), having sliders 54!, 542, 543, and 544 respectively. The sliders 54!, 542, 543, and 544 are driven by shafts 545, 546, 541, and 548, that are positioned through suitable gearing 55! in accordance with the time of flight as determined by shaft 455. It is understood that the shaft 455 may be driven by the output shaft of any of the three time of flight mechanisms heretofore described.

As was stated in connection with the description of the gyro unit, the difference in the voltages of leads 225 and 226 relative to ground is proportional to the torque applied by the azimuth torque motor 56, and hence is proportional to the angular rate of movement of the spin axis 68 of the gyro rotor 61, which corresponds to the angular rate of movement of the target in a lateral plane (2A5). These voltages are applied to the potentiometers 221 and 228, respectively. Since the sliders 54! and 542 are positioned in accordance with the time of flight (To) the difference of the voltages of sliders 54! and 542 as represented by leads 553 and 554 is proportional to the lateral prediction angle (AAS).

Similarly, the voltage difference of leads 23! and 232 is proportional to the torque applied by the elevation torque motor 18 and hence is proportiona1 t0 the angular rate (2E5) of movement of the target in a vertical plane including the line of sight. Sliders'543 and 544 are rotated in accordance with a time of flight (Tc) so the output voltage difference as represented by leads 555 and 556 is proportional to the slant elevation prediction angle (AE5). The voltage of leads 553 and 554 and leads 555 and 556, representing the lateral and slant elevation prediction angles respectively, are supplied to a conversion unit 560 (Fig. 3) where they are converted to azimuth and elevation prediction angles.

Conversion unit 7 From an inspection of Fig. 2, it will be apparent that the lateral prediction angle (AAS), which is obtained by multiplying the angular rate (EAS) in a lateral plane by the present time of flight (To) is quite different to the azimuth prediction angle (AAh), which must be added to the observed angle (A0) in order to obtain future azi- 20 muth angle (Ap). Similiarly, the slant eleva'-' tion prediction angle (AE5), which is obtained by multiplying the angular rate (2E5) of the target by the present time of flight (To) is quite different to the elevation prediction angle (AEn), which must be added to the observed elevation angle (E0) to obtain the future elevation angle (Ep) of the predicted position of the target.

By trigonometric construction it may be shown that the elevation prediction angle (AEh) has a definite relation to the slant elevation prediction angle (AE5) and that this relation is dependent upon. the elevation angle as well as the prediction angles; A similar arrangement is disclosed in Patent No. 2,423,821 to Garbarini et al., issued July 15, 1947.

The value of the azimuth prediction angle (AAh) may be expressed as follows:

tan AA cos (EM-AB) wherein AE is the vertical prediction angle in a vertical plane including the line of sight. It can also be shown that the future elevation angle (E13), that is, the sum of the observed elevation angle (E0) and the elevation prediction angle (AEh) is represented by the following equation:

(7) E =sin- [sin (Eo-i-AE) cos AAs] sin AE cos AA,

For the small size of the slant elevation prediction angle (AES) and the vertical prediction angle (AE) it can be assumed that the angles are equal to their sines and that sin AE:

(9) cos AA,

which may be further approximated as 7 AB, AE= (M10 2 Since the value of the slant elevation prediction angle (AE5) is obtained in terms of the difference of two voltages, that is, voltage (AEsl) represented by lead 555 (Fig. 4b) (AEsz) represented by lead 556, it is possible to solve Equation 5 electrically in order to obtain the valueof the vertical prediction angle (AE).

The voltage (AEsl) on lead 555 is connected to both ends of a potentiometer 56 and the voltage (AESZ) represented by lead 556 is connected to both terminals of potentiometer 562. The sliders 563 and 564 of the potentiometers 56! and 562, respectively, are rotated in accordance with the lateral prediction angle (AAS) by motor 565,

which rotates shaft 566 to drive shafts 561 and 568 through suitable gearing 569 and 51!.

The lateral prediction angle motor 565 is operated in the following manner to rotate shaft 566 in accordance with the lateral prediction angle (AAS). The lateral prediction angle (AAS) is represented by the difference in the voltages appearing on leads 553 and 554. Lead 5'54 is connected through resistor 515 to grid 512 of tube 513, which is arranged in a balanced amplifier circuit with a similar tube 514. Lead 553 is applied to 2i grid 516 of the tube 514 through a resistor 511 in a similar manner. The plates of tubes 513 and 51 5 are connected through opposite halves of winding 518 of the lateral prediction angle motor 565 to a suitablesource of positive potential, such as battery 519. The cathodes of the two tubes are connected through a common cathode resistor 58! to a negative voltage 592, which provides a definite normal current through the two tubes and the opposite halves of the winding 518.

The shaft 565, which is rotated by the lateral prediction angle motor 565, drives through gearing 585 to rotate shaft 585 and slider 586 of potentiometer 581, that has its terminals connected to a battery 588, the midpoint of which is grounded. The slider 555 is connected through a resistor 581 to the grid 512.

If the voltages applied to the grids 512 and 515 are unequal, unequal currents flow through the two halves of the winding 518, causing the lateral prediction angle motor 555 to rotate in a direction I that will move the slider 586 until the voltage on the grid 512 is made equal to that on the grid 516 by combining a positive or negative voltage with the voltage appearing on lead 553. It will be apparent, therefore, that the shaft 556 is rotated in accordance with the lateral prediction angle (AAS) The voltages of sliders 563 and 564 are applied through resistors 59! and 592, which are equal and referred to as R2, to grids 593 and 59 3 of tubes 595 and 595, which are arranged in a balanced amplifying circuit with their cathodes 591 and 593 connected through a resistor 599 to a source of negative potential such as battery 9!, thus normally providing a definite current through each of the tubes.

Plates 692 and 593 of the tubes 595 and 595 are connected through opposite halves of winding 595 of the vertical prediction angle (AE) motor 555 to a source of positive potential, such as battery 606.

The vertical prediction angle motor 65 drives through gearing 991 to rotate a shaft 698, which positions slider 699 of potentiometer 5i i, which has its terminals connected to a battery 5l2, the midpoint of which is grounded. The voltage in the slider 69'! will hereinafter be referred to as the vertical prediction angle voltage (AE).

The circuit of tubes 595 and 596 in motor 695 is so arranged that the motor drives the potentiometer slider 699 until its voltage when added to or subtracted from the voltage from the potentiometer slider 563 equals the voltage from the potentiometer slider 564. The vertical prediction angle voltage as determined by slider 609 is connected through a resistor 9I5 to grid 594. The resistor 915 has a value hereinafter referred to as R1, which is equal to resistor 615, connected between the grid 593 of the tube 595 and ground.

When the motor 595 is in equilibrium and the voltage of grid 594 equals the voltage of grid 593, the voltages in the circuit may be represented by the following equation:

AESZ represents the voltage of lead 556 from the prediction unit, the voltage AEsl is equal to the voltage of lead 555 from the prediction unit, re-

sistance R1 is equal to the values of resistors 515 and 6E5, resistance R3 is equal to the effective resistance of potentiometers 56! and 562 between 22 lead 555 and slider 563 and between lead 556 and slider 56 (since sliders 593 and 564 are driven in unison the effective voltages of the potentioni eters are equal), and the resistance R2 is equal to the values of resistances 59l and 592.

Since the difference of the voltages AE'SZ and AEsl, that is, the difference of the voltages of leads 555 and 556, is equal to a voltage that is proportional to the slant elevation prediction angle (AE5) this equation may be written as follows:

As the actual resistance of potentiometers 55! and 552 between their terminals has a value of Rp, the effective resistance R3 between the leads 555 and 555 and sliders 559 and 564 may be represented by the following equation:

in which K1 represents the unit of resistance of potentiometer windings and 0 represents the angle by which the slider is moved from the center-point of potentiometer winding. By substituting this value of R3, we have:

R K1202 13 R +R i 72,?

R1 R, which may be rewritten as:

R2 R MA Then by substituting in the Equation 12, we have:

provided that the constant K2 is introduced by the gearing 601 of the vertical prediction angle motor Since the solution of Equation 17 for the vertical prediction angle (AE) is the same as the trigonometric expression of Equation 10, it will be apparent that the vertical prediction angle motor 605 rotates in accordance with the vertical prediction angle (AE) when the circuit is balanced, that is, when the voltage of grid 593 equals the voltage of grid 594. r

The output of the vertical prediction angle motor 605 is geared through sutable gearing 621 to a shaft 622, which represents one input of a differential 623.

Shaft I21 of the gyro unit (Fig. 4a) is rotated in accordance with the observed elevation angle of the target, and this shaft is connected through gearing 625, shaft 526, and gearing 521 to shaft I21, which is also rotated in accordance with the observed elevation angle (E) The shaft I21 drives through gearing 629 to rotate shaft 66!, forming a second input of the differential 623. Thus, an output shaft 632 of the differential 623 is rotated in accordance with the sum (EO+AE) of the observed elevation angle (E0) and the vertical prediction angle (AE). This output shaft drives through gearing 633 to rotate a shaft 634 carrying an elongated pinion 635 which meshes with a gear 636 on three-dimensional cam 631 to rotate the cam 631 together with a three-dimensional cam 638 in accordance with the sum (E0+AE) of observed elevation angle and vertical prediction'angle. The shaft 566, which is rotated in accordance with the lateral prediction angle (AA drives through gearing 64!, shaft 642, pinion 643, and rack 644 to translate the three-dimensional cams 638 and 631 in accordance with the lateral prediction angle (AA Since the three-dimensional cam 631 is translated in accordance with the lateral prediction angle (AA and is rotated in accordance with the sum (Eo-l-AE) of the observed elevation angle and the vertical prediction angle, its surface may be so arranged that follower 646 riding thereon has a lift corresponding to the azimuth prediction angle (AAh) as determined by Equation 6.

Similarly, since cam 638 is rotated in accordance with the sum (EH-AB) of the observed elevation angle and the vertical prediction angle and is translated in accordance with the lateral prediction angle (AA its surface may be so laid out that follower 641 has a lift corresponding to the future elevation angle (E as determined by Equation 7 From the foregoing description it will be apparent that the slant elevation prediction angle (AE and the lateral prediction angle .(AA have been converted into elevation and azimuth prediction angles by first electrically converting the slant elevation prediction angle (AE into the vertical prediction angle (AE), and then by combining the vertical prediction angle (AE) with the lateral prediction angle (AA and the observed elevation angle (E0) to obtain a future elevation angle (Ep) and azimuth prediction angle (AAh). The azimuth prediction angle may then be added to the Observed azimuth angle (A0) to determine the future azimuth angle (A The follower 646 has a rack 66!] which engages a pinion 648 to rotate shaft 649, which forms one input of differential 651, in accordance with the azimuth prediction angle (AAh). The other input of the differential 66! is rotated in accordance with the observed azimuth angle (A0) by shaft H2 so the output of the differential 65! as represented by shaft 652 is rotated in accord ance with the sum (An-l-AAh) of the observed azimuth and azimuth prediction angles, that is, the future azimuth angle (A Follower 641 translates a rack 654 which meshes with pinion 665 to rotate shaft 666 in accordance with the future elevation angle (Ep).

The conversion mechanism described has taken the lateral prediction angle and the slant elevation prediction angle in terms of electrical voltages and converted them into future azimuth and future elevation angles in terms of shaft displacement. If the lateral prediction and the slant elevation prediction angles are available in terms of shaft displacements, the conversion unit may be modified to convert these shaft displacements into future azimuth and future elevation angles, also in terms of shaft displacements.

One modified form of a conversion unit for mechanically computing the vertical prediction angle (AE) and determining the azimuth prediction angle (AAh) and the future elevation angle (E is shown in Fig. I. If a lateral prediction angle (AAS) and the slant elevation prediction angle (AES) are available in the form of shaft displacements, they may be driven into the modified conversion unit by shafts 66! and 662, respectively. The shaft 66l drives through suitable gearing 663 to rotate shaft 664 which drives through pinion 665 to translate a rack 666 carrying three-dimensional cams 661 and 668. The shaft 664 also drives through a second pinion 669 to translating rack 61| carrying a three-dimensional cam 612.

An elongated pinion 613 on the shaft 662 meshes with a gear 614 to rotate the cam 612 in accordance with the slant elevation prediction angle (AE5).

It may be shown trigonometrically that the vertical prediction angle (AE) has the following definite relation with the lateral prediction angle (AAS) and the slant elevation prediction angle (AE5) (l8) AE=sin (sin AES sec AAS) Since the cam 612 is translated according to the lateral prediction angle (AAS) and rotated in accordance with slant elevation prediction angle (AE5), it may be so designed that a follower 615 riding on the surface thereof has a lift corresponding to the vertical prediction angle (AE) in accordance with Equation 18. A rack 616 on the follower 615 meshes with a pinion 611 to drive a shaft 618 in accordance with the vertical prediction angle (AE). The shaft 618 forms one input of a differential 619, the other input of which is driven by a shaft 66! in accordance with the observed elevation angle (E0) which may be driven by the shaft I21 from the elevation servomotor of the gyro shown in Fig. 4A.

The differential 619 has an output shaft 682,

which is thus rotated in accordance with the sum (Eo-l-AE) of the observed elevation angle and the vertical prediction angle. shaft 682 drives through suitable gearing 663 to rotate a shaft 684 and an elongated pinion 685 which meshes with a gear 666 to rotate the cams 661 and 668 inaccordance with the sum (Ea-i-AE').

Since the cam 661 is translated in accordance with the lateral prediction angle (M55) and rotated in accordance with the sum (Eo+AE)', a follower 68B riding on the surface thereof is displaced in accordance with the azimuth prediction angle (.AAh) as determined by Equation 6. A rack 686 on the follower 618 drives through a pinion 69! to rotate a shaft 692 from one input of the differential 693 in accordance with the azimuth prediction angle (AAh). The other input of the differential 663 is driven by shaft 694 in accordance with the observed azimuth angle as determined by the gyro unit. Thus, output shaft 666 of the diiferential 693 is rotated in accordance with the sum (Ao-i-AAh) which is equal to the future azimuth anglem The cam 668 is also rotated in accordance with the sum (Eo-l-AE) and translated in accordance with the lateral prediction angle (AAS). The surface of the cam 668 may be so laid out that a follower 6S6 riding on its surface has a lift corresponding to the future elevation angle (Ep) in accordance with Equation '7. However, in order to provide a better scale factor, the surface of the cam 668, since it is rotated in accordance dicated air speed of the craft.

indicated air speed is introduced into the com- 2.

25 with the sum (EotAE), has this sum subtracted from its surface whereby the follower 696 is actually displaced in accordance with the expression The follower 695 has a rack 69! which drives a pinion 698 to rotate a shaft 699 forming one input of a differential fill, in accordance with the above expression. A shaft H52 forming a second input of the differential lfil is driven by shaft 682 through suitable gearing H33 in accordance with the sum (Eo-j-AE). Thus, output shaft H34 of the differential H3! is driven in accordance with the future elevation angle (Ep).

It will be apparent that the mechanism described utilizes the lateral prediction angle (AAS) the slant elevation prediction angle (AE5), and the observed azimuth and elevation angles (A0) and (E0) to determine future azimuth and elevation angles (Ap) and by which shafts 695 and :24 are rotated. The shafts 695 and 164 correspond to the shafts 652 and 656 of the conversion unit described in connection with Fig. 4B.

Either of the foregoing conversion units may be used to determine the future azimuth and elevation angles.

Ballistic correction unit The computer mechanism thus far described has taken data obtained by tracking the target in range, azimuth and elevation, and used this data to compute the future position of the target in terms of future azimuth and elevation angles. It is now only necessary to correct these future azimuth and elevation angles for ballistic effect on the projectile after it leaves the gun in order to determine the azimuth and elevation angle at which the guns must be positioned to hit the target.

A ballistic unit H I (Fig. 3) considers two major factors in determining ballistic correction angles. These factors are the effects of windage and of gravity. The effect of windage jump has been omitted from the ballistics unit HI because it was found that this effect is small and may be omitted without seriously affecting the operation of the computer.

The main windage effect is considered to be the wind force acting on the projectile during its flight to the target and thus deflecting the projectile from its original path. The total deflection due to this force is dependent upon the future range of the target, the velocity of the wind. acting upon the projectile, the density of the air, and the angle of the projectiles path relative to the direction of the wind. The futurerange of the target, that is, the distance which a projectile must travel, may be computed from the values of range and range rate which are determined by the range computer 251.

The velocity of the wind acting upon the projectile may be computed as a function of the in- This function of puter by a mechanism which will hereinafter be described. The density of air is a function of altitude and is introduced into the ballistics unit by the same mechanism that supplied a function of altitude to the time of flight unit 385.

Functions of future range, indicated air speed, and altitude, may be combined to determine the approximate windage force acting on a projectile. It is then only necessary to determine the effect of these forces upon the projectile, which is a function of the gun position angles. In order to correct the future azimuth and elevation angles which have been computed, it is necessary to determine lateral and vertical components of the ballistic correction angle. The force acting on the projectile may be resolved into vertical and lateral components. Each of these components depends upon the same variables of future range, indicated air speed, and altitude, and their resolution depends upon gun azimuth and gun elevation angles.

In the ballistics unit H l, as shown'in detail in Fig. 4b, an approximate value of future range is determined as a function of range (D0) and range rate (D As was discussed in connection with the time of flight unit 385, the ratio of future range (Dp) to present range (Do) is approximately constant for a given range rate (Do). Hence, the future range may be expressed as the product of the present range (D0) and a function of range rate (D The windage force acting on the projectile may be expressed as the product of a function of future range, a function of indicated air speed, and a function of altitude. In order to determine the lateral ballistic deflection, it is only necessary to combine the force with a predetermined function of the gun azimuth angle (Ag) and the gun elevation angle (Eg), whereas the vertical windage deflection angle (6E) may be expressed as the product of a function of the future range, a function of indicated air speed, and a function of altitude, combined with different functions of the gun azimuth angle (A and gun elevation angle (Eg). The vertical deflection angle thus computed does not consider the effect of gravity, which must be subsequently combined with the vertical deflection angle (6E) to obtain the superelevation angle (s) From the foregoing description it follows that the windage force acting on the projectile may be expressed as the product of functions of range (Do), range rate (D indicated air speed (IAS) and altitude (H). This force ma be obtained most easily by adding the logarithms of the four functions involved.

Referring to Fig. 3, the mechanism for introducing indicated air speed will now be described. A hand wheel H5, which may be located in the pilots or navigators compartment, is adjusted to set in a logarithmic function of indicated air speed by rotating shaft H 8, which positions rotor winding ill of a self-synchronous transmitter H8. Obviously, the shaft H5 could be set automatically by a suitable air speed measuring device. The winding 1 I l is supplied from a suitable source, such as that shown at H9. The transmitter H8 has a stator winding F20 connected to secondary winding E2! of a self-synchronous receiver E22, whereby a voltage is induced in rotor winding T23 of the receiver :22, having a phase relation with the voltage of source I I 9 corresponding to the angular displacement between shaft H6 and a shaft 72%, which positions the rotor 123.

A servomotor drives through worm gear T25 and worm wheel F2? to rotate shaft 128, which in turn drives through gearing 129 to position shaft in accordance with the desired logarithmic function of indicated air speed. The operation in control of servomotor 125 is substantially the same as that described in connection with the control of the altitude motor 414. The voltageof winding I23 is compared in phase with the voltage of a source I32, which is synchronized with the source l I9, as by a phase detecting circuit including tubes 133 and I34. The output voltage across resistors I35 and 1351s supplied through condenser and resistance differentiating networks I31 and I38, and applied to the grids of amplifying tubes I39 and MI, having their plate circuits connected to opposite halves of winding I42 of the motor I25, whereby the motor rotates the winding I23 of receiver I22 until the phase of the voltage across the winding I23 corresponds to that of the source I32.

The shaft 13! supplied the logarithmic function of indicated airspeed to the ballistic unit III and drives through gearing 145 to rotate -shaftI lIi, forming one input of a differential 'I4'I inaccordance with the logarithmic function of indicated air speed. The shaft 424, which has already been described, is rotated in accordance with the logarithmic function of altitude, and drives one input of differential I48 of the ballistic unit H I. The other input of the differential I48, as represented by shaft I49, is driven through gearing II, shaft I52, and gearing I53 by the shaft 256, which is rotated in accordance With logarithmic function of range (Do) as was described in connection with the range computer unit L The output of differential I48 rotates shaft I55 which drives a second input of the differential M1. The output of the differential Ml, which is represented by shaft I58, drives one input of differential I51. The shaft 88!, which has also been described in connection with the range computing unit, is positioned in accordance with a function of range rate, and drives through gearing I58 to rotate shaft I59, forming a second input of the differential I51.

It will be apparent that the differentials M8 and 141 add logarithmic functions of altitude (H), range (D0), and indicated air speed (IAS), whereby the output shaft 155 of differential I41 is rotated in accordance with the sum of these logarithmic functions. This sum of logarithmic functions is combined with the function of range rate in differential 151. The logarithmic function of range rate within the limits used in this computer is substantially linear. Hence, it is unnecessary to obtain the logarithmic function of range rate to be added to the other logarithmic functions, as the same result is accomplished by adding a more or less linear function of range rate. However, if the limits of the computer are increased to the point where a logarithmic function of range rate is necessary, it may easily be obtained by substituting a logarithmically wound potentiometer for the linear potentiometer 312 in the range rate motor control circuit of the range computer unit 25L If a logarithmic potentiometer is used, the range rate motor 352 is rotated in accordance with a logarithmic function of range rate.

'An output shaft I85 of the differential I51 drives through gearing I62 to rotate shaft H53 in accordance with the sum of the four functions combined by the differentials I58, I41, and I51. An elongated pinion I64 meshes with a gear I65 on a cylindrical cam 166 having an antilogarithmic cam groove 557 formed in its surface, and engaged with a stationary cam pin I68. Since the gear F55 rotates the cylinder I56 in accordance with the sum of the four logarithmic functions represented by the output shaft l6I, the cylinder I66 is translated in accordance with the product of these four functions by the action of the cam groove and pin.

Lil

The cylinder IE5 is connected with cams Ill and 112 to also translate them in accordance with the product of these functions. The cams Ill and 112 are rotated by an elongated pinion I13, which meshes with a gear I14 and is driven by shaft 115 through suitable gearing I16 and shaft 'III in accordance with the gun azimuth angle (Ag) in a manner to be subsequently described. A follower I18 riding on the surface of cam I12 translates cam 119 in accordance with a function of gun azimuth (Ag), which isthe desired function for determining the lateral ballistic correction angle. The cam I19 is rotated by an elongated pinion I8I, meshing with a gear I82, by a shaft I83 corresponding to the gun elevation angle (Eg) in a manner which will subsequently be described. A follower I84 riding on the surface of the cam I19 has a lift corresponding to the lateral windage deflection correction angle and acts through rack T85 and pinion 186 to rotate shaft I81 in accordance with the lateral windage deflection angle, which is equal to the lateral ballistic correction angle (6A) Similarly, a follower I89 riding on the surface of the cam 'II I is positioned in accordance with the product of a predetermined function of the gun azimuth angle (A and the functions rep resenting the force acting on the projectile. The follower 189 translates a cam IQI, which is also rotated in accordance with the gun elevation angle (Eg) by an elongated pinion I8I, which meshes with a gear I92, whereby a follower I93 riding on the surface of the cam I9I is displaced in accordance with the vertical windage deflection angle (6E). A rack I94, formed on the follower I93, meshes with a pinion I95 to rotate a shaft 196 in accordance with the vertical windage deflection angle (5E).

By combinin the gravity correction angle with the vertical windage deflection angle, it is possible to obtain a vertical ballistic correction angle which, when combined with the future elevation angle, provides the gun elevation angle desired.

The force of gravity is effective only in the vertical plane; hence, only affects the vertical correction angle. The total gravity deflection depends upon the time of flight and the gun elevation angle. This may be expressed in terms of a constant which includes the gravitational force, the time of flight, and the gun elevation angle (Eg). For this purpose, the present time of flight (To) is sufficiently accurate and is supplied to the ballistic unit by a shaft Bill which is driven by the shaft 45I through gearing 802 and acts through pinion 803 and rack 804 to translate a three-dimensional cam in accordance with the time of flight (To). A gear 886 on the three-dimensional cam 805 meshes with elongated pinion 88! on the shaft I83 to rotate the cam 805 in accordance with the gun elevation angle (Ag). Thus, follower 889, riding on the surface of the cam 885, is displaced in accordance with the grayity'deflection angle (G) and acts through rack 8H and pinion 8I2 to rotate shaft 8I3, forming an input of the differential 8M.

One input of the differential 8 is driven in accordance with the vertical windage deflection angle (5E), whereby the output, as represented by shaft M5, is rotated in accordance with the total elevation ballistic correction angle or superelevation angle ($5). The shaft 8I5 drives through gearing BIB to position shaft 8, forming one input of a differential 8I8 in accordance with the superelevation angle ((#5). The other input of differential 8H3 is driven by the shaft 655 in accordance with the future elevation angle (Ep) whereby the output as represented by shaft 819 is rotated in accordance with the gun elevation angle (Eg). 1

The shaft 8l9 positions a rotor winding 82! of a suitable self-synchronous transmitter 822 that is energized from a source 823. The transmitter 822 has a stator winding 824 that is connected with a stator winding 825 of a suitable receiver 826, having a rotor 827 that is positioned in accordance with position of shaft 828, which is driven through suitable gearing 825 by a gun elevation motor 83 I.

The gun elevation motor 83! is controlled to rotate shaft 828 until the position of rotor 82'! corresponds to the position of rotor 82I as determined by comparing a source of reference voltage 832 with the voltage across the winding 821 as by suitable phase detecting tubes 833 and 834, which are connected through smoothing networks 835 and 836 to control amplifying tubes 83'! and 838. The plate circuits of tubes 83'! and 838 are connected through the opposite halves of winding 83!! of the motor 83!, whereby the motor drives in one direction or another depending upon the sense of the phase displacement of the voltage across winding 28! as compared with reference voltage 832.

The motor 83I drives shaft 828 until its position corresponds with the position of shaft 819. The motor 83I thereby positions shaft 183 in accordance with the gun elevation angle (Eg) and drives gun elevation into the ballistic correction mechanism to rotate cams I79, I91, and 805, as has already been described.

The shaft 181, which is rotated in accordance with the lateral ballistic correction angle. (6A), drivesthrough gearing 84!, shaft 842, and gear 843 to rotate a shaft 855, forming one input of differential 846, in accordance with the lateral ballistic correction angle (6A). The other input of the differential 3% is driven by shaft 652 in accordance with the future azimuth angle (A whereby output shaft 84'! is positioned in accordance with the gun azimuth angle (Ag), which positions rotor winding 848 of a self-synchronized transmitter 849 that is energized by a suitable source 85 l. The transmitter 849 has a stator winding 852 connected to stator 853 of a selfsynchronized receiver 854, which has a rotor 855 positioned by a, shaft 856 that is driven through suitable gearing 85! by a gun azimuth angle motor'858.

The motor 353 is controlled by phase detecting tubes 859 and 852 in a manner similar to that described in the gun elevation angle motor 83L Tubes S59 and 682 are connected through smoothing networks 853 and 35 to control amplifying tubes 355 and 856 which are connected to opposite halves of winding 36'? of the motor 85%, whereby the motor rotates to position shaft 858 in accordance with the position of shaft 847 as determined by comparing the phase of voltage across rotor winding 855 of the receiver 854 with a reference voltage from a source 859.

The shaft 855 drives through suitable gearing 8H to rotate shaft ill in accordance with the gun azimuth angle (A and thus position cams l?! and T72.

Shafts 828 and representing the gun elevation angle (Eg) and gun azimuth angle (Ag), may be used to position the guns in any suitable manner as by positioning self-synchronous transmitters 873 and 814 which are connected by cables 8'55 and 816 to suitable servo mechanisms (not shown).

Summary The computer which constitutes the subject matter of this invention thus utilizes rates determined by the precession torques applied to a gyro in tracking a target, together with the ob served azimuth and elevation angles of the target, the range of the target, and the altitude and indicated air speed of the aircraft, to determine the angles at which guns on th craft must be positioned in order to direct a projectile toward a predicted future position of the target.

In summary. referring again to Fig. 3, signals either from the hand control 28 or the radio sight H are supplied through switch 2| to the gyro unit 23, which controls suitable amplifiers for the application of torques by torque motors on the two axes of the gyro. Voltages proportional to the torque applied, representing lateral and vertical rates of movement of the target, are supplied to prediction unit 229.

The range computer 25! is controlled either by range foot pedal 24% to position stadia lines 1'53, or by the automatic radio range 3 H of the radio sight H to determine a logarithmic function of range (Do) as represented by shaft 295 and a function of range rate (1'3 as represented by shaft 38L The range computer also computes the time of flight in a vacuum, which is a linear function of the range (Do) and is equal to the range divided by the muzzle velocity. This is supplied by shaft 623 to the time of flight unit 385. The time of flight unit 385 utilizes the logarithmic function of range (Do) as supplied by shaft 285, the logarithmic function of altitude as supplied by shaft 524, which is controlled by hand'wheel 38-3 in a remote compartment, and the observed azimuth angle (A0) which is supplied by shaft H2 from the gyro unit 23 and shaft #328. The time of flight unit computes the product of functions of range (D0), observed azimuth (A0), and altitude (H) to determine the change in time of flight due to prevailing conditions. This change in time of flight is combined with the time of flight in a vacuum to provide a time of flight (To) to the present position of the target as repbe substituted for the time of flight unit 385. The prediction unit 229 combines the lateral and vertical rates (2A3 and BBQ) with the time of flight (To) to obtain a lateral prediction angle AA) and a slant elevation prediction angle (AE5).

Values of these angles are supplied in electrical form to the conversion unit where they are combined with the observed elevation angle (E0) as represented by shaft 62f from the gyro unit 23 and introduced by shaft 63! into the conversion unit 568. The conversion unit determines the azimuth prediction angle (AAh) as represented by rotation of shaft 659, which is combined with the observed azimuth angle (A0) in the difierential 65| to determine the future azimuth angle (Ap). The other output of the conversion unit is the future elevation angle (E which is represented by shaft 656.

The ballistics unit HI is supplied with a logarithmic function of range (Do) by shaft "M9, which is driven through shaft 286; a function of range rate (D which is represented by shaft 

